Simulations of Point Processes on Directed Graphs

Sammanfattning: Simulating a point process where the events correspond to vehicle collisions on a road networkcan be quite computationally heavy due to the large number of elements that are necessary toprovide a sufficient discretization of the network. This paper aims to present a computationallyefficient solution for simulating events of a point process. With this goal in mind, an end to endapplication is developed that starts by constructing a discretization of the road graph to represent the state space of the process and associating accidents with elements of the roadgraph, and goes on to simulate events of the process from one or more realisations. The simulation of events is done in a two-level approach; first the arrival times are obtained via inversion and then the incidents are located on the graph by sampling from the conditional distribution of the states given the arrival times. Even though the state space is constructed fromhundreds of thousands of edges and vertices, the application is relatively efficient in terms of computing time and given enough compute nodes in a distributed computing framework is ableto scale to arbitrarily large state spaces. Future work shall revolve around a finer partitioning of the road network and the incorporation of additional characteristics of the events, under a marked point process.